Volume 18, issue 1 (2014)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Commutative ring objects in pro-categories and generalized Moore spectra

Daniel G Davis and Tyler Lawson

Geometry & Topology 18 (2014) 103–140
Abstract

We develop a rigidity criterion to show that in simplicial model categories with a compatible symmetric monoidal structure, operad structures can be automatically lifted along certain maps. This is applied to obtain an unpublished result of M J Hopkins that certain towers of generalized Moore spectra, closely related to the K(n)–local sphere, are E–algebras in the category of pro-spectra. In addition, we show that Adams resolutions automatically satisfy the above rigidity criterion. In order to carry this out we develop the concept of an operadic model category, whose objects have homotopically tractable endomorphism operads.

Keywords
Moore spectra, pro-objects, structured ring spectra, endomorphism operad
Mathematical Subject Classification 2010
Primary: 55P43, 55U35
Secondary: 18D20, 18D50, 18G55
References
Publication
Received: 22 August 2012
Revised: 7 April 2013
Accepted: 13 June 2013
Preview posted: 21 November 2013
Published: 9 January 2014
Proposed: Bill Dwyer
Seconded: Haynes Miller, Paul Goerss
Authors
Daniel G Davis
Department of Mathematics
University of Louisiana at Lafayette
1403 Johnston Street
Maxim Doucet Hall, Room 217
Lafayette, LA 70504-1010, USA
http://www.ucs.louisiana.edu/~dxd0799/
Tyler Lawson
Department of Mathematics
University of Minnesota
206 Church St SE
Minneapolis, MN 55455, USA
http://math.umn.edu/~tlawson/